A353677 a(n) = 1 if n is an odd number of the form p^j * q^k, with p and q primes and gcd(phi(p^j), phi(q^k)) = 2, otherwise 0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0

Offset

1

Comments

A necessary condition for a(n) = 1 is that at least one of the prime factors of n is of the form 4*m + 3 (A002145). - David A. Corneth, May 04 2022

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = A000035(n) * A353678(n).

a(n) <= A353676(n).

Prog

(PARI) A353677(n) = if(!(n%2)||(2!=omega(n)), 0, my(f=factor(n)); (2==gcd(eulerphi(f[1, 1]^f[1, 2]), eulerphi(f[2, 1]^f[2, 2]))));

Crossrefs

Characteristic function of A329229.

Cf. A000010, A000035, A002145, A007774, A353676, A353678.

Sequence in context: A354989 A277161 A353481 * A353676 A391238 A340370

Adjacent sequences: A353674 A353675 A353676 * A353678 A353679 A353680

Keyword

nonn

Author

Antti Karttunen, May 03 2022

Status

approved